Find the product of (4x − 3)(x + 2).

4x2 + 5x − 6
4x2 − 5x − 6
4x2 + 11x − 6
4x2 − 11x − 6

Answer:

Step-by-step explanation:

[tex]y=\frac{1}{2} x+2[/tex]

[tex]y=(x-h)^2+k[/tex]

[tex]y=(x+3)^2-2=x^2+6x+7[/tex]

The minor arc in the given diagram as required to be determined is; arc TU and it's measure is; 116°.

The major arc in the given diagram as required to be determined is; arc TVU and it's measure is; 244°.

It follows from the task content that the minor and major arcs are to be named and their measures determined as required.

The minor arc in a circle is usually subtended by an angle less than 180° while the major arc is subtended by an angle greater than 180°.

Ultimately, the minor arc is; arc TU and it's measure is; 116° while the major arc is; arc TVU and it's measure is; 244°.

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Answer:

Step-by-step explanation:

Answer:

y = -45

Step-by-step explanation:

y=mx+b

because the graph is horizontal m = 0

y=0x+b --> y=b

next sub in points

y=b (9,-45)

-45=b

therefore equation is y=-45

(a) f'(7) = 9. The derivative of the function f(x) evaluated at x=7, is 9.

(b) The instantaneous rate of change of y with respect to x at x = 7 is 9.

Given that the tangent line to the graph of y = f(x) at point (7, 56) has the equation y = 9x - 7, we can use the slope-intercept form of the equation of a line to find the slope of the tangent line.

The slope of the tangent line is 9. This is also equal to the derivative of the function f(x) evaluated at x=7, which gives us the answer to part (a).

The instantaneous rate of change of y with respect to x at x = 7 is also given by the derivative of the function at x=7. Therefore, the answer to part (b) is also f'(7) = 9.

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The vertices of ∆A′B′C′ are A′(-6, 5), B′(-6, 8), and C′(-10, 5) upon the application of the translation rule.

What is the translation rule in geometry?

In geometry, a translation is a transformation that moves every point of a figure the same distance in the same direction. In the case of a triangle, a translation rule describes how to move each vertex of the triangle to a new location to create a new triangle with the same size and shape, but in a different position.

A translation rule for a triangle is given by a pair of numbers (a, b), which indicate the amount of horizontal and vertical movement of the vertices. Specifically, the rule is given by the formula:

(x, y) → (x + a, y + b)

This formula means that we move every point in the triangle a unit to the right or left (depending on the sign of a) and b units up or down (depending on the sign of b).

The translation rule (x, y) → (x − 3, y + 4) means that we move every point in the original triangle left by 3 units and up by 4 units. So, the translation is described as a leftward shift of 3 units and an upward shift of 4 units.

To find the vertices of ∆A′B′C′, we apply the translation rule to each vertex of ∆ABC:

Vertex A: (x, y) → (x - 3, y + 4)

(-3, 1) → (-3 - 3, 1 + 4) = (-6, 5)

So, vertex A of ∆A′B′C′ is located at (-6, 5).

Vertex B: (x, y) → (x - 3, y + 4)

(-3, 4) → (-3 - 3, 4 + 4) = (-6, 8)

So, vertex B of ∆A′B′C′ is located at (-6, 8).

Vertex C: (x, y) → (x - 3, y + 4)

(-7, 1) → (-7 - 3, 1 + 4) = (-10, 5)

So, vertex C of ∆A′B′C′ is located at (-10, 5).

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The complete question is as follows:

Answer:

Based on the given information in the box plots, the statement that is best supported is that Steven spent more time studying than Martha did during the week for their math final exam. This can be inferred because the top line of Steven's box plot is higher than the top line of Martha's box plot, indicating that Steven spent more time studying than Martha in the given time period. Additionally, Steven's whisker extends higher than Martha's whisker, further supporting the idea that Steven studied for a longer period of time than Martha.

To determine if the proportion is true or false, we can cross-multiply and see if the equation holds:

16 miles / 18 quarts = 24 miles / 27 quarts

Cross-multiplying, we get:

16 miles * 27 quarts = 18 quarts * 24 miles

432 milesquarts = 432 milesquarts

The equation holds, so the proportion is true.

The proportion is true .

To determine if the proportion is true or false, we can cross-multiply and see if the equation holds:

16 miles / 18 quarts = 24 miles / 27 quarts

Cross-multiplying, we get:

16 miles * 27 quarts = 18 quarts * 24 miles

432 milesquarts = 432 milesquarts

Proportion can be checked by simplifying the ratios given,

16miles/18quarts=24miles/27quarts​

Simplifying further,

8miles/9squarts = 8miles / 9squarts .

The equation holds, so the proportion is true.

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In triangle ABC, the values of AB and BC are 9.68 and 7.04 respectively i.e. A.

What is a triangle's definition?

A triangle is a geometric form that has three straight sides and three angles. It is a fundamental geometric form that is frequently utilised in mathematics, science, and everyday life.

Triangles are distinguished by three sides and three angles. The sum of each triangle's three angles is always 180 degrees. Triangles are classified according to the length of their sides and the measurement of their angles.

Now,

As given ΔDEF ≈ΔABC

that means ratio of all sides will be equal

i.e. AB/DE=BC/EF=AC/DF

then AB/8.8=6.71/6.1

AB=1.1*8.8

AB=9.68

and BC/6.4=6.71/6.1

BC=1.1*6.4

BC=7.04

Hence,

            the values of AB and BC are 9.68 and 7.04 respectively.

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The projectile will attain a height of 85 feet at approximately 0.775 seconds or 3.225 seconds.

Given that

Velocity = 64 feet per second --- v

Initial height = 45 feet --- h

The height function can be represented as

h(t) = -16t² + vt + h

So, we have

h(t) = -16t² + 64t + 45

where h is the height in feet and t is the time in seconds.

To find when the projectile will attain a height of 85 feet, we need to solve the equation for t

So, we have

-16t² + 64t + 45 = 85

-16t² + 64t - 40 = 0

Using a graphing tool, we have

t = 0.775 and t = 3.225

Therefore, the projectile will attain a height of 85 feet at approximately t = 0.775 seconds or t = 3.225 seconds.

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Solution,

CP for rajan=180 rs

Sp for rajan=(20%+1)×180

=216

Cp for niranjan=216

And, Sp=.8×216

=172.8

Cp for niranjan=172.8

For 5% profit,

Sp for Niranjan=(5%+1)×172.8

=181.44

Hence, for Niranjan to gain 5% profit, he must sell it for 181.44 rs

Answer - 181.44

Explanation - For Rajan,

Cost Price = Rs 180

Profit Percent = 20%

Profit Percent = (S.P - C.P/C.P)*100

20 = (S.P - 180/180) *100

S.P = Rs 216

For Sajan,

C.P = Rs 216

Loss Percent= 20%

Loss = (C.P - S.P/C.P)*100

20 = (216-S.P/216)*100

S.P = Rs 172.8

For Niranjan to Sell Book and get 5% profit,

C.P = Rs 172.8

Profit Percent = (S.P - C.P/C.P)*100

5 = (S.P-172.8/172.8)*100

S.P = 181.44

Answer:

25 + 5√29

Step-by-step explanation:

(I added a photo below)

First, let's find BC using the Pythagorean theorem (from ∆BCD):

[tex] {bc}^{2} = {25}^{2} + {10}^{2} = 625 + 100 = 725[/tex]

[tex]725 > 0[/tex]

[tex]bc = \sqrt{725} =5 \sqrt{29} [/tex]

Then we see, that AB = 25 + x

So, now we can find AC:

[tex] {ac}^{2} = ({25 - x})^{2} - ({5 \sqrt{29} })^{2} = 625 - 50x + {x}^{2} - 25 \times 29 = 625 - 50x + {x}^{2} - 725 [/tex]

Now we have a quadratic equation:

[tex] {x}^{2} - 50x - 100 = 0[/tex]

[tex]d = {b}^{2} - 4 \times a \times c = ({ - 50})^{2} - 4 \times 1 \times ( - 100) = 2500 + 400 = 2900 > 0[/tex]

[tex]x1 = \frac{ - b - \sqrt{d} }{2a} = \frac{50 - 10 \sqrt{29} }{2} = 25 - 5 \sqrt{29} [/tex]

This is a negative number and we cannot use it, since x has to be a natural number

[tex]x2 = \frac{ - b + \sqrt{d} }{2 a} = \frac{50 + 5 \sqrt{29} }{2} = 25 + 5 \sqrt{29} [/tex]

The problem can be translated into an equation as follows: 8x = (1/3)(x+2)

the answer that represents this situation is: 8x = (1/3)(x+2)

Simplifying the right side of the equation:

8x = (1/3)x + (2/3)

Multiplying both sides of the equation by 3 to eliminate the fraction:

24x = x + 2

Subtracting x from both sides of the equation:

23x = 2

Dividing both sides of the equation by 23:

x = 2/23

Therefore, the answer that represents this situation is:

8x = (1/3)(x+2)

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Answer:

[tex]31+4x > 63[/tex]

To reach her fitness goal, she needs to run for more than 8 days.

Step-by-step explanation:

She has already run 31 miles and runs 4 miles per day:

This means that after x days, the distance she will have run is:

[tex]D(x)=31+4x[/tex]

Tammy must run more than 63 miles total to reach her fitness goals.

This means that:

[tex]D(x) > 63[/tex]

[tex]31+4x > 63[/tex]

The inequality is:

[tex]31+4x > 63[/tex]

Solution:

[tex]4x > 32[/tex]

[tex]x > \dfrac{32}{4}[/tex]

[tex]x > 8[/tex]

To reach her fitness goal, she needs to run for more than 8 days.

The missing values in the figure are solved to be

angle KLI = 111

angle LIJ = 129 degrees

The missing angles are solved using the inscribed angle theorem and the knowledge of cyclic quadrilateral

arc KLI = 138 degrees = 2 * angle KJI (inscribed angle theorem)

angle KJI = 138 / 2

angle KJI = 69 degrees

angle KLI + angle KJI = 180 degrees (cyclic quadrilateral property)

where angle KJI = 69

angle KLI = 180 - 69

angle KLI = 111 degrees

angle LIJ + angle LKJ = 180 degrees (cyclic quadrilateral property)

angle LKJ = 51 degrees (given)

angle LIJ = 180 - 51

angle LIJ = 129 degrees

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Thus, the obtained expression for the perimeter of the rectangle in centimeters is found as: P =  2(11v + 5w) cm.

The perimeter of a rectangle is the length measured around the edge of the rectangle. Although a rectangle has two dimensions, its perimeter only has one and is expressed in linear distances like feet or meters.

The perimeter calculation can be used, for instance, to calculate that many ft of brick border are required overall if somehow the rectangle depicts a garden which needs a brick border.

The sum of the lengths of a rectangle's four sides is known as its perimeter.

Rectangle perimeter = 2L + 2W.

Length = (6v+7w)

width = (5v - 2w)

P = 2 (length  + width)

P = 2(6v+7w + 5v - 2w)

On simplifying:

P =  2(11v + 5w)

Thus, the obtained expression for the perimeter of the rectangle in centimeters is found as: P =  2(11v + 5w) cm.

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Compete question:

The width of a rectangle measures (5v - 2w) centimeters, and its length measures (6v+7w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?​

The height of the building is 160 ft

Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios.

Types of  proportion :

Direct Proportion

Inverse Proportion

Continued Proportion

Comparing the heights and shadows using ratio proportions

Sam Height = 8 ft

Sam Shadow = 10 ft

Building Height = x ft

Building Shadow = 200 ft

Sam Height/Sam Shadow = Building Height/Building Shadow

AB/BC = PQ/QR

8/10 = x/200

8*200 = 10*x

1600/10 = x

x = 160 ft

The height of the building is 160 ft

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Answer:

Step-by-step explanation:

16 × 19 = 304

1/2(19×9)=85.5

304-85.5= 218.5

Answer:

21.5 m^2

Step-by-step explanation:

Area of circle A = πr^2 = 3.14(10/2)^2 = 78.5

Area of square A = 10^2 = 100

Area of shaded area: 100 - 78.5 = 21.5 m^2

The Area οf the shaded pοrtiοn is given by (16 π -32) inch², the cοrrect οptiοn is A.

A circIe is a rοund shaped figure whοse aII pοints Iie in οne pIane and the distance between the center οf the circIe and aII the pοints οn the circIe is cοnstant.

The area οf the shaded pοrtiοn is equaI tο the difference οf the area οf the arc and  Area οf the TriangIe.

Area οf an Arc =(θ /360) × π r²

Area = (90/360) × π × (8)²

Area οf the arc = 16 π in²

Area οf the triangIe = (1/2) × base × height

Area οf the triangIe = (1/2) × 8 × 8 = 32 in²

Area οf the shaded pοrtiοn = (16 π -32) inch²

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Option B. The length of the hypotenuse of Carter's triangle is 13cm.

Since Carter's triangle is similar to Peyton's triangle, the ratio of corresponding side lengths will be the same. Let's use x to represent the length of the hypotenuse of Carter's triangle.

We know that the ratio of the lengths of the hypotenuse and the shorter leg of Peyton's triangle is 13:5. So, the ratio of the lengths of the hypotenuse and the shorter leg of Carter's triangle must also be 13:5.

Thus, we have x/5 = 13/5, which simplifies to x = 13.

Therefore, the length of the hypotenuse of Carter's triangle is 13cm.

Therefore, the only possible length for Carter's hypotenuse is 13cm, and the correct answer is A.

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Peyton drew a right triangle with sides 5cm, 12cm, and 13cm long. Carter drew a similar triangle to Peyton’s. Which of the following can be the measurements of Carter’s triangle?

A. 15cm

B. 13cm

C. 11cm

D. 10cm

A graph of the image of ABC under a dilation whose center is P and scale factor is 1/2 is shown in the image below.

In Geometry, a dilation can be defined as a type of transformation which typically changes the size of a geometric shape, but not its shape.

In this exercise, we would use an online graphing calculator to plot the image of ABC after a dilation by a scale factor of 1/2 centered at P.

Based on the image (see attachment), we can logically deduce that each vertex is 1/2 times as far from center P as the original vertex and each segment is 1/2 times as long as the original:

Side length A'C' = 8.2/2 = 4.1

Side length A'B' = 5.7/2 = 2.85

Side length B'C' = 12.2/3 = 6.1

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a. The percentage of persons (p) who would permit the pressure to increase to its highest point is what we are predicting.

What is the statistics

b.the pressure to build to its highest point (75/264).

c. Sample statistic's value is 0.2835.

d. Estimate's standard error is 0.0255.

e. Its highest level, the 95% confidence interval, is (0.2326, 0.3344).

A subfield of mathematics called statistics is concerned with the gathering, examination, interpretation, presentation, and arrangement of data.

Several disciplines, including business, economics, sociology, psychology, epidemiology, and public health, employ it. Statistic uses a variety of techniques to gather and analyse data to better understand.

(A) The percentage of persons (p) who would permit the pressure to increase to its highest point is what we are predicting.

(b) The sample statistic, given as p, is the percentage of subjects that allowed the pressure to build to its highest point (75/264).

(c) The sample statistic's value is 0.2835.

(d) The estimate's standard error is 0.0255.

(e) For the percentage of people who would permit the pressure to reach its highest level, the 95% confidence interval is (0.2326, 0.3344).

Therefore, Overall, the findings of this study indicate that a significant majority of high school pupils will tolerate pressures up to 300 mmHg without ever complaining about the discomfort. The range of values inside the 95% confidence.

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Answer:

25/4 quarts of cranberry juice

40/3 quarts of apple juice

25/8 quarts of lemonade

Step-by-step explanation:

just multiply everything by 5

:)

Answer:

-8

Step-by-step explanation:

f(3) = -4(3) + 4 = -12 + 4 = -8

Answer:

Step-by-step explanation:

[tex]\boxed{\sf f(x) = -4x + 4 \;\: when \;\; x=3}[/tex]

For f(x) -4x+4 substitute x with 3:-

[tex]\sf f\left(3\right)\:=\:-4(3)\:+\:4[/tex]

[tex]\sf f\left(3\right)\:=\:-4\times 3\:+\:4[/tex]

[tex]\sf f(3)=-12+4[/tex]

[tex]\sf f(3)=-8[/tex]

Therefore, f(x) = -8.

______________________

Hope this helps!

The revenue is maximized for a value p = 100, and the maximum revenue is:

R =  23,500

We know that the number of items sold for a prize p is:

-2.35p + 470

Then the revenue will be:

R = (-2.35p + 470)*p

So we need to find the value of p that maximizes that quadratic equation, we can see that the maximum will be at the vertex, then let's write:

R = -2.35p² + 470p

The vertex is at:

p = -470/(2*2.35)

p = 100

Finally, the maximum revenue is:

R =  -2.35*100² + 470*100

R = 23,500

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Answer: 156

Step-by-step explanation:

Annual Salary = $35, 000

Subtract anual salary from 46, 700. ---> 46,700-35,000= 11,700

One sale = $75

To find out how many sales, divide the remaining 11,700 by 75.

11,700/75= 156

156 sales.